The problem is that it was reported - as you say erroneously - as if it was to do with the BC sexism issue, where it appears to be something entirely separate. Perhaps the story was misconstrued, perhaps people jumped to conclusions based on the details they had on the story and the things already in the public which led to it being reported that way. I certainly thought from the article I read on it that it referred back to the Halford's days or the national team, and my post on the Sutton thread that you c+ped into here for context was based on that understanding.
Personally, I haven't read Lizzie's book, so I can only run on what has been reported, so if I've only perpetuated a misconception, then that's my bad. I also am not in any position to comment on which stories have been circulated into the press and which haven't, because I don't know what other stories the book deals with. The issue is that I'm not a fan of hers, personally, and rightly or wrongly she has given me the impression throughout her career of being somebody out for themselves and who has a tendency when things don't go her way to find somebody else to blame; quick to take the credit when it goes right, quick to apportion blame when it doesn't. The fallout from the testing thing, both among fans and, critically, among the women's péloton, showed that I'm far from alone in my interpretation of her, which runs counter to the image that has been attempted to be presented, whether by her or by others (certainly the way she has wanted to present herself has not always run harmoniously with the image others have wanted to present of her). As a result I always find her more prepared (i.e. not heat-of-the-moment) interviews to come across as disingenuous, and the way you describe her book ("It is therefore wholly regrettable that she says so little about actual sport itself in the pages of Steadfast, has so little to say about actual races, and instead uses the book to settle some petty scores and engage in an exercise in reinvention") suggests to me not an inconsiderable amount of opportunism and barely-disguised PR which is one of the things that's always made her seem unlikable to me; trying to prevent the tide of PR turning against her and dissociating herself from potentially harmful associations if the walls start to crumble while simultaneously being scathing of those who fought against the tide long before her (which is how I interpret your summation) isn't all that surprising. Because pettiness, blaming others, and pushing a favorable agenda is exactly what I would expect from her, and therefore I don't think I could enjoy reading her book, nor could I read it while maintaining objectivity.